CN102764929A - Elliptical orbit directional tangential line constant-speed welding robot device - Google Patents

Abstract

The invention discloses an elliptical orbit directional tangential line constant-speed welding robot device, and belongs to the technical field of welding robot. The elliptical orbit directional tangential line constant-speed welding robot device comprises a mechanical arm, a Z shaft rotary table, a controller, a welding power supply and a welding gun, wherein the mechanical arm is formed by connecting an X shaft translation component with a Y shaft translation component in series; a workpiece with an elliptical orbit weld joint is controlled to rotate along with a workpiece installation table; and the welding gun is controlled to move along with the X shaft translation component and the Y shaft translation component. In the device, an individually moving three-degree-of-freedom mechanism is adopted, the high-quality welding function on the elliptical orbit weld joint of the workpiece is realized; when welding is carried out by adopting the device, the welding gun is always located at a normal at the welding point part on the elliptical orbit weld joint, the welding direction is the tangential line direction of the elliptical orbit, and the tangential line faces to certain preset fixed direction, the welding speed keeps constant, the welding quality is high, the efficiency is high, and the device is low in manufacturing, maintaining and using costs; and at each point in welding, the welding gun and the welding point of the weld joint on the workpiece keep certain opposite position and posture, thus the optimized welding effect can be achieved.

Description

The directed tangent line constant speed of elliptical orbit welding robot device

Technical field

The invention belongs to the Technology of Welding Robot field, the structural design of the directed tangent line constant speed of particularly a kind of elliptical orbit welding robot device.

Background technology

In space flight, aviation, boats and ships and field of petrochemical industry, there are various equipment in a large number with ellipse arc.In the production process of equipment, need workpiece be welded along elliptic segment trajectory.In order to obtain high-quality weld seam; Need reach following a plurality of target simultaneously during the workpiece welding: welding gun requires to be in all the time the downhand position during welding; Welding gun all the time straight down; And welding direction is consistent in the tangential direction of this point with elliptical path, and this tangent line is necessary for horizontal line, and it is constant that speed of welding keeps.At present, the artificial welding manner of the many employings of the welding of elliptical orbit, minority also has 6 drag articulation type industrial robots of employing to weld.Workman's technical merit is required height for the former and working strength of workers is big, welding efficiency is low, and welding quality is difficult for guaranteeing; Latter's complex equipments is produced and the maintenance cost height.

Summary of the invention

The objective of the invention is the weak point to prior art, the directed tangent line constant speed of a kind of elliptical orbit welding robot device is provided, this device can conveniently be realized the welding to workpiece elliptical orbit weld seam; When adopting this device to weld; Welding gun is on the elliptical orbit weld seam at the normal at pad place all the time, and welding direction is the tangential direction of elliptical orbit, and this tangent line is all the time towards the welding quality that preestablishes on certain fixed-direction to guarantee to obtain to optimize; It is constant that speed of welding keeps; Welding quality is high, and efficient is high, and the manufacturing of device, maintenance and use cost are low.

Technical scheme of the present invention is following:

The directed tangent line constant speed of a kind of elliptical orbit provided by the invention welding robot device is characterized in that: comprise mechanical arm, Z axle turntable, controller, the source of welding current and welding gun; Said mechanical arm comprises X axle translation assembly and the Y axle translation assembly that is together in series successively; The axis of a weld of workpiece to be welded is an elliptical orbit;

Said X axle translation assembly comprises first pedestal, X spindle motor, X shaft transmission and first slide block; The said X spindle motor and first pedestal are affixed, and the output shaft of said X spindle motor links to each other with the input of X shaft transmission, and the output of said X shaft transmission links to each other with first slide block, and said first slide block slides and is embedded on first pedestal;

Said Y axle translation assembly comprises second pedestal, y-axis motor, Y shaft transmission and second slide block; Said second pedestal and first slide block are affixed; The said y-axis motor and second pedestal are affixed, and the output shaft of said y-axis motor links to each other with the input of Y shaft transmission, and the output of said Y shaft transmission links to each other with second slide block, and said second slide block slides and is embedded on second pedestal;

Said Z axle turntable comprises the 3rd pedestal, Z spindle motor, Z shaft transmission, joint shaft and workpiece erecting bed; Said the 3rd pedestal and first pedestal are affixed; Said Z spindle motor and the 3rd pedestal are affixed; The output shaft of said Z spindle motor links to each other with the input of Z shaft transmission; The output of said Z shaft transmission links to each other with joint shaft, and said joint shaft is movably set in the 3rd pedestal, and said workpiece erecting bed is fixedly sleeved on joint shaft;

Said welding gun is installed on second slide block, and welding gun links to each other with the source of welding current; Said X spindle motor, y-axis motor and Z spindle motor link to each other with controller respectively; Said controller links to each other with the source of welding current; Need the workpiece of welding to be fixedly mounted on the workpiece erecting bed; The weld seam that has elliptical orbit on the workpiece;

If said first slide block is straight line q with respect to the glide direction of first pedestal; If said second slide block is straight line s with respect to the glide direction of second pedestal; If the center line of said joint shaft is straight line u; Straight line q, straight line s and straight line u three are vertical in twos; If straight line q and straight line s constitute plane Q ₁, the plane, elliptical orbit place of establishing axis of a weld on the workpiece is plane Q ₂, plane Q ₁With plane Q ₂Overlap;

Controller control X spindle motor, y-axis motor and Z spindle motor rotate simultaneously;

{ C}, { initial point of C} is the center O of joint shaft to said world coordinate system to set up world coordinate system _C, world coordinate system { the transverse axis x of C} _CQ is parallel with straight line, x _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that first slide block slides with respect to first pedestal, the world coordinate system { longitudinal axis y of C} _CS is parallel with straight line, y _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that second slide block slides with respect to second pedestal, and { C} and the 3rd pedestal are affixed for this world coordinate system;

{ A}, { initial point of A} is the center O of elliptical orbit to said elliptical coordinate system to set up elliptical coordinate system _A, elliptical coordinate system { the transverse axis x of A} _AOverlap the elliptical coordinate system { longitudinal axis y of A} with transverse _AOverlap with ellipse short shaft, { A} is affixed with the workpiece of band elliptical orbit weld seam for said elliptical coordinate system;

Point O _C{ coordinate figure among the A} is (d in elliptical coordinate system _x, d _y), (d _x, d _y) be known constant;

If speed of welding is preset value v _w, establishing workpiece, to rotate counterclockwise angular speed around joint shaft be ω; If a is major axis half the of said elliptical orbit, b is minor axis half the of said elliptical orbit; If the major axis of said elliptical orbit and x _CThe angle of axle is θ, 0≤θ≤90 °; The center line of said welding gun and y _CAxle is parallel, and the center line of welding gun and the intersection point of elliptical orbit are solder joint P; { coordinate among the C} is (X to said solder joint P at world coordinate system _C, Y _C); { coordinate among the C} is (X if the distal point T of welding gun is at world coordinate system _TC, Y _TC); The distal point T of said welding gun and the distance of solder joint P are preset value L _aThe distal point T of welding gun and solder joint P are along x _CThe speed of axle equates, is v ₁, relative world coordinate system { C}; The distal point T of welding gun and solder joint P are along y _CThe speed of axle equates, is v ₂, relative world coordinate system { C};

Controller control workpiece and welding gun satisfy following relationship:

$X_C=\frac{(a^2-b^2)\sin \mathrm{\θ}}{\sqrt{a^2{\tan }^2\mathrm{\θ}+b^2}}-d_x\cos \mathrm{\θ}+d_y\sin \mathrm{\θ},$

$Y_C=\sqrt{a^2{\tan }^2\mathrm{\θ}+b^2}\cos \mathrm{\θ}-d_x\sin \mathrm{\θ}-d_y\cos \mathrm{\θ},$

X _TC=X _C,

Y _TC=Y _C+L _a,

$\mathrm{\β}=\arctan \left(\frac{Y_C}{X_C}\right),$

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{X_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">C</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;})}^2}},$

v ₁=Mω，

v ₂=Nω，

Wherein,

$M=\frac{(a^2-b^2)(b^2-a^2{\mathrm{<figure-callout\; id="4"\; label="tan"\; filenames="HDA00001919831000031.png,HDA00001919831000032.png"\; state="\{\{state\}\}">tan</figure-callout>}}^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\mathrm{<figure-callout\; id="2"\; label="tan"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">tan</figure-callout>}}^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\mathrm{<figure-callout\; id="2"\; label="tan"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">tan</figure-callout>}}^2\mathrm{\&theta;}+b^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;},$

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: said X shaft transmission adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: said Y shaft transmission adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: said Z shaft transmission is a reductor.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: also comprise wire-feed motor, controller links to each other with wire-feed motor, and wire-feed motor links to each other with welding gun.

The directed tangent line constant speed of another kind of elliptical orbit provided by the invention welding robot device is characterized in that: comprise mechanical arm, Z axle turntable, controller, the source of welding current and welding gun; Said mechanical arm comprises X axle translation assembly and the Y axle translation assembly that is together in series successively; The axis of a weld of workpiece to be welded is an elliptical orbit;

Said X axle translation assembly comprises first pedestal, X spindle motor, X shaft transmission and first slide block; The said X spindle motor and first pedestal are affixed, and the output shaft of said X spindle motor links to each other with the input of X shaft transmission, and the output of said X shaft transmission links to each other with first slide block, and said first slide block slides and is embedded on first pedestal;

Said Y axle translation assembly comprises second pedestal, second slide block and plane pressing plate; Said second pedestal and first slide block are affixed; Said second slide block slides and is embedded on second pedestal; The said plane pressing plate and second slide block are affixed; Said plane pressing plate contacts with workpiece, and the lower surface and the elliptical orbit of plane pressing plate are tangent; The lower surface of said plane pressing plate is a horizontal plane;

Said Z axle turntable comprises the 3rd pedestal, Z spindle motor, Z shaft transmission, joint shaft and workpiece erecting bed; Said the 3rd pedestal and first pedestal are affixed; Said Z spindle motor and the 3rd pedestal are affixed; The output shaft of said Z spindle motor links to each other with the input of Z shaft transmission; The output of said Z shaft transmission links to each other with joint shaft, and said joint shaft is movably set in the 3rd pedestal, and said workpiece erecting bed is fixedly sleeved on joint shaft;

Said welding gun is installed on second slide block, and welding gun links to each other with the source of welding current; Said X spindle motor links to each other with controller respectively with the Z spindle motor; Said controller links to each other with the source of welding current; Need the workpiece of welding to be fixedly mounted on the workpiece erecting bed; The weld seam that has elliptical orbit on the workpiece;

If said first slide block is straight line q with respect to the glide direction of first pedestal; If said second slide block is straight line s with respect to the glide direction of second pedestal; If the center line of said joint shaft is straight line u; Straight line q, straight line s and straight line u three are vertical in twos; If straight line q and straight line s constitute plane Q ₁, the plane, elliptical orbit place of establishing axis of a weld on the workpiece is plane Q ₂, plane Q ₁With plane Q ₂Overlap;

Controller control X spindle motor and Z spindle motor rotate simultaneously;

{ C}, { initial point of C} is the center O of joint shaft to said world coordinate system to set up world coordinate system _C, world coordinate system { the transverse axis x of C} _CQ is parallel with straight line, x _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that first slide block slides with respect to first pedestal, the world coordinate system { longitudinal axis y of C} _CS is parallel with straight line, y _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that second slide block slides with respect to second pedestal, and { C} and the 3rd pedestal are affixed for this world coordinate system;

{ A}, { initial point of A} is the center O of elliptical orbit to said elliptical coordinate system to set up elliptical coordinate system _A, elliptical coordinate system { the transverse axis x of A} _AOverlap the elliptical coordinate system { longitudinal axis y of A} with transverse _AOverlap with ellipse short shaft, { A} is affixed with the workpiece of band elliptical orbit weld seam for said elliptical coordinate system;

Point O _C{ coordinate figure among the A} is (d in elliptical coordinate system _x, d _y), (d _x, d _y) be known constant;

If speed of welding is preset value v _w, establishing workpiece, to rotate counterclockwise angular speed around joint shaft be ω; If a is major axis half the of said elliptical orbit, b is minor axis half the of said elliptical orbit; If the major axis of said elliptical orbit and x _CThe angle of axle is θ, 0≤θ≤90 °; The center line of said welding gun and y _CAxle is parallel, and the center line of welding gun and the intersection point of elliptical orbit are solder joint P; { coordinate among the C} is (X to said solder joint P at world coordinate system _C, Y _C); { coordinate among the C} is (X if the distal point T of welding gun is at world coordinate system _TC, Y _TC); The distal point T of said welding gun and the distance of solder joint P are preset value L _aThe distal point T of welding gun and solder joint P are along x _CThe speed of axle equates, is v ₁, relative world coordinate system { C}; The distal point T of welding gun and solder joint P are along y _CThe speed of axle equates, is v ₂, relative world coordinate system { C};

Controller control workpiece and welding gun satisfy following relationship:

$X_C=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

$Y_C=\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;},$

X _TC=X _C,

Y _TC=Y _C+L _a,

$\mathrm{\&beta;}=\arctan \left(\frac{Y_C}{X_C}\right),$

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{X_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">C</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;})}^2}},$

v ₁=Mω，

v ₂=Nω，

Wherein,

$M=\frac{(a^2-b^2)(b^2-a^2{\mathrm{<figure-callout\; id="4"\; label="tan"\; filenames="HDA00001919831000031.png,HDA00001919831000032.png"\; state="\{\{state\}\}">tan</figure-callout>}}^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\mathrm{<figure-callout\; id="2"\; label="tan"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">tan</figure-callout>}}^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\mathrm{<figure-callout\; id="2"\; label="tan"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">tan</figure-callout>}}^2\mathrm{\&theta;}+b^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;},$

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: said X shaft transmission adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: said Z shaft transmission is a reductor.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: also comprise wire-feed motor, controller links to each other with wire-feed motor, and wire-feed motor links to each other with welding gun.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device, it is characterized in that: also comprise spring spare (81), the two ends of said spring spare connect second slide block and second pedestal respectively, and said spring spare adopts extension spring, stage clip, torsion spring or sheet spring.

The present invention compared with prior art has the following advantages and the high-lighting effect:

This device adopts the Three Degree Of Freedom mechanism of self-movement to realize workpiece elliptical orbit weld seam high-quality welding function, and when adopting this device to weld, welding gun is on the elliptical orbit weld seam normal at the pad place all the time; Welding direction is the tangential direction of elliptical orbit; And towards preestablishing on certain fixed-direction, it is constant that speed of welding keeps all the time for this tangent line, and welding quality is high; Efficient is high, and the manufacturing of device, maintenance and use cost are low; Because the every bit in welding, the weld seam solder joint on welding gun and the workpiece all remains a kind of relative position and attitude, therefore can reach the high-quality welding effect of optimization; The direction that sets can be an any direction, for example: when elliptical orbit is on the vertical facade, welding gun is kept in the vertical direction, and welding direction remains and go up in the horizontal direction, thereby obtain the high-quality welding effect of downhand position; For example: when elliptical orbit is on the horizontal plane, welding gun and welding direction is all remained simultaneously go up in the horizontal direction, thereby obtain the high-quality welding effect of horizontal position.

Description of drawings

Fig. 1 is the three-dimensional view of a kind of embodiment of the directed tangent line constant speed of elliptical orbit of the present invention welding robot device.

Fig. 2 is front appearance figure embodiment illustrated in fig. 1.

Fig. 3 is a side view embodiment illustrated in fig. 1.

Fig. 4 is the annexation sketch map of middle controller embodiment illustrated in fig. 1, the source of welding current, welding gun, X spindle motor, y-axis motor and Z spindle motor.

Fig. 5 is the three-dimensional view of the another kind of embodiment of the directed tangent line constant speed of elliptical orbit of the present invention welding robot device.

Fig. 6 is front appearance figure embodiment illustrated in fig. 5.

Fig. 7 is a side view embodiment illustrated in fig. 5.

Fig. 8 is the annexation sketch map of middle controller embodiment illustrated in fig. 5, the source of welding current, welding gun, X spindle motor and Z spindle motor.

Fig. 9 is the principle schematic that the coordinate system of two kinds of embodiment of the directed tangent line constant speed of elliptical orbit of the present invention welding robot device is set up situation, each parameter geometrical relationship.

Figure 10 is that coordinate system is set up the situation sketch map in the concrete example calculation, and in this example, the initial point of world coordinate system is just on the positive axis of the longitudinal axis of elliptical coordinate system.

Figure 11 is a fine motion analysis principle sketch map, and among the figure, solid line is a current location, and dotted line is the position after joint shaft rotates a d θ angle.P ₁Being current solder joint, also is the peak on the current elliptical orbit, and the center line of welding gun is positioned at the normal direction of this some place elliptical orbit, P ₁' be the position of current solder joint after joint shaft rotates a d θ angle on the workpiece, P ₂Be the next solder joint after d θ angle of joint shaft rotation, this new solder joint also is the peak of elliptical orbit when next position, and the center line of that moment welding gun still is positioned at the normal direction of new solder joint place elliptical orbit.

Figure 12, Figure 13, Figure 14, Figure 15 be respectively through formula according to the invention and θ, ω, the X of an example calculating of the pointwise calculation procedure method of giving _C, Y _C, v ₁, v ₂Respectively with the relation curve of time t.

In Fig. 1 to Figure 15:

1-X axle translation assembly, 11-first pedestal, the 12-X spindle motor,

The 13-X shaft transmission, 14-first slide block,

2-Y axle translation assembly, 21-second pedestal, the 22-Y spindle motor,

The 23-Y shaft transmission, 24-second slide block,

3-Z axle turntable, 31-the 3rd pedestal, the 32-Z spindle motor,

The 33-joint shaft, 34-workpiece erecting bed, the 35-Z shaft transmission,

The 4-controller, the 5-source of welding current, the 6-welding gun,

61-welding gun center line, the 70-workpiece, 71-elliptical orbit weld seam,

8-plane pressing plate, the 81-spring, the 9-wire-feed motor,

Q-first slide block is with respect to the straight line of the glide direction of first pedestal;

S-second slide block is with respect to the straight line of the glide direction of second pedestal;

The straight line of the center line of u-joint shaft;

{ C}-world coordinate system, the initial point O of this world coordinate system _CBe the center of joint shaft, transverse axis x _CFor level to the right, longitudinal axis y _CFor straight up, this world coordinate system and the 3rd pedestal are affixed;

{ A}-elliptical coordinate system, the initial point O of this elliptical coordinate system _ABe the center of elliptical orbit, transverse axis x _ABe transverse place direction, longitudinal axis y _ABe ellipse short shaft place direction, this elliptical coordinate system is affixed with the workpiece of band elliptical orbit;

v _w-speed of welding is preset value, is the relative velocity of welding gun with respect to workpiece;

Half of the major axis of a-elliptical orbit, a is known constant;

Half of the minor axis of b-elliptical orbit, b is known constant;

( ^Ad _x, ^Ad _yThe distance at the center of)-elliptical orbit and the center of joint shaft, d is known constant;

The major axis of θ-elliptical orbit and x _CThe folded acute angle of axle, also be the workpiece of the band elliptical orbit weld seam angle of rotating around the center line of joint shaft with workpiece erecting bed, joint shaft (when angle is 0, the major axis of elliptical orbit and x _CAxle is parallel);

The current solder joint of P-, or be called current point of contact is the intersection point of elliptical orbit weld seam on center line and the workpiece of welding gun, also is the maximum Y of elliptical orbit under current turned position _CThe value point;

The distal point of T-welding gun,

L _aThe distal point T of-welding gun and the distance of solder joint P (be similar to arc length, will influence arc length), L _aBe preset value;

(X _C, Y _C)-solder joint P is at the world coordinate system { coordinate figure among the C};

(X _TC, Y _TCThe distal point T of)-welding gun is at the world coordinate system { coordinate figure among the C};

β-solder joint P and joint shaft center O _CLine and x _CThe acute angle that axle is folded, in Fig. 7, β=∠ PO _Cx _C

v ₁The distal point T of-welding gun and point of contact P are along x _CThe movement velocity of axle positive direction is with respect to world coordinate system { for the C};

v ₂The distal point T of-welding gun and point of contact P are along y _CThe movement velocity of axle positive direction is with respect to world coordinate system { for the C};

The workpiece of ω-band elliptical orbit weld seam is around the center O of joint shaft _CThe angular speed that rotates counterclockwise is with respect to world coordinate system { for the C};

v ₃-workpiece is in the linear velocity at solder joint P place, with respect to world coordinate system { for the C};

v _x, v _y-workpiece is at the linear velocity v at solder joint P place ₃Respectively along x _CAxle and y _CThe speed of decomposing is with respect to world coordinate system { for the C};

M, N-write for simple formula, the intermediate variable of employing.

The specific embodiment

Further introduce the content of concrete structure of the present invention, operation principle in detail below in conjunction with accompanying drawing and a plurality of embodiment.

A kind of embodiment of the directed tangent line constant speed of elliptical orbit provided by the invention welding robot device like Fig. 1, Fig. 2, Fig. 3 and shown in Figure 4, comprises mechanical arm, Z axle turntable 3, controller 4, the source of welding current 5 and welding gun 6; Said mechanical arm comprises the X axle translation assembly 1 and Y axle translation assembly 2 that is together in series successively; The axis of a weld of workpiece 70 to be welded is an elliptical orbit 71;

Said X axle translation assembly 1 comprises first pedestal 11, X spindle motor 12, X shaft transmission 13 and first slide block 14; The said X spindle motor 12 and first pedestal 11 are affixed, and the output shaft of said X spindle motor 12 links to each other with the input of X shaft transmission 13, and the output of said X shaft transmission 13 links to each other with first slide block 14, and said first slide block 14 slides and is embedded on first pedestal 11;

Said Y axle translation assembly 2 comprises second pedestal 21, y-axis motor 22, Y shaft transmission 23 and second slide block 24; Said second pedestal 21 and first slide block 24 are affixed; The said y-axis motor 22 and second pedestal 21 are affixed, and the output shaft of said y-axis motor 22 links to each other with the input of Y shaft transmission 23, and the output of said Y shaft transmission 23 links to each other with second slide block 24, and said second slide block 24 slides and is embedded on second pedestal 21;

Said Z axle turntable 3 comprises the 3rd pedestal 31, Z spindle motor 32, Z shaft transmission 35, joint shaft 33 and workpiece erecting bed 34; Said the 3rd pedestal 31 and first pedestal 11 are affixed; Said Z spindle motor 32 and the 3rd pedestal 31 are affixed; The output shaft of said Z spindle motor 32 links to each other with the input of Z shaft transmission 35; The output of said Z shaft transmission 35 links to each other with joint shaft 33; Said joint shaft 33 is movably set in the 3rd pedestal 31, and said workpiece erecting bed 34 is fixedly sleeved on joint shaft 33;

Said welding gun 6 is fixedly mounted on second slide block 24, and welding gun 6 links to each other with the source of welding current 5; Said X spindle motor 12, y-axis motor 22 link to each other with controller 4 respectively with Z spindle motor 32; Said controller 4 links to each other with the source of welding current 5; Need the workpiece 70 of welding to be fixedly mounted on the workpiece erecting bed 34; The weld seam 71 that has elliptical orbit on the workpiece;

If said first slide block 14 is straight line q with respect to the glide direction of first pedestal 11; If said second slide block 24 is straight line s with respect to the glide direction of second pedestal 21; If the center line of said joint shaft 33 is straight line u; Straight line q, straight line s and straight line u three are vertical in twos; If straight line q and straight line s constitute plane Q ₁, the plane, elliptical orbit 71 place of establishing axis of a weld on the workpiece 70 is plane Q ₂, plane Q ₁With plane Q ₂Overlap;

Controller 4 is controlled X spindle motor 12, y-axis motor 22 and Z spindle motor 32 and is rotated simultaneously;

As shown in Figure 7, { C}, { initial point of C} is the center O of joint shaft to said world coordinate system to set up world coordinate system _C, world coordinate system { the transverse axis x of C} _CQ is parallel with straight line, x _CThe positive direction of axle is to leave the direction of elliptical orbit 71, also is the positive direction that first slide block 14 slides with respect to first pedestal 11, the world coordinate system { longitudinal axis y of C} _CS is parallel with straight line, y _CThe positive direction of axle is to leave the direction of elliptical orbit 71, also is the positive direction that second slide block 24 slides with respect to second pedestal 21, and { C} and the 3rd pedestal are affixed for this world coordinate system;

{ A}, { initial point of A} is the center O of elliptical orbit to said elliptical coordinate system to set up elliptical coordinate system _A, elliptical coordinate system { the transverse axis x of A} _AOverlap the elliptical coordinate system { longitudinal axis y of A} with transverse _AOverlap with ellipse short shaft, { A} is affixed with the workpiece of band elliptical orbit weld seam for said elliptical coordinate system;

Point O _C{ coordinate figure among the A} is (d in elliptical coordinate system _x, d _y), (d _x, d _y) be known constant; A kind of special case is: the said elliptical coordinate system { longitudinal axis y of A} _ACenter O through said joint shaft _C, then put O _CElliptical coordinate system the coordinate figure among the A} be (0, d _y); Shown in Figure 10 for working as a some O _CAt the elliptical coordinate system { longitudinal axis y among the A} _APositive axis on situation;

If speed of welding is preset value v _w, establishing workpiece 70, to rotate counterclockwise angular speed around joint shaft 33 be ω; If a is major axis half the of said elliptical orbit 71, b is minor axis half the of said elliptical orbit 71; If the major axis of said elliptical orbit 71 and x _CThe angle of axle is θ, 0≤θ≤90 °; The center line of said welding gun 6 and y _CAxle is parallel, and the intersection point of the center line of welding gun 6 and elliptical orbit 71 is solder joint P; { coordinate among the C} is (X to said solder joint P at world coordinate system _C, Y _C); { coordinate among the C} is (X if the distal point T of welding gun 6 is at world coordinate system _TC, Y _TC); The distal point T of said welding gun 6 and the distance of solder joint P are preset value L _aThe distal point T of welding gun 6 and solder joint P are along x _CThe speed of axle equates, is v ₁, relative world coordinate system { C}; The distal point T of welding gun 6 and solder joint P are along y _CThe speed of axle equates, is v ₂, relative world coordinate system { C};

Controller 4 control workpiece 70 satisfy following relationship with welding gun 6:

$X_C=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

$Y_C=\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;},$

X _TC=X _C,

Y _TC=Y _C+L _a,

$\mathrm{\&beta;}=\arctan \left(\frac{Y_C}{X_C}\right),$

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;})}^2}},$

v ₁=Mω，

v ₂=Nω，

Wherein,

$M=\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;},$

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device is characterized in that: said X shaft transmission 13 adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

In embodiment illustrated in fig. 1, said X shaft transmission 13 adopts the feed screw nut transmission mechanism.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device is characterized in that: said Y shaft transmission 23 adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

In embodiment illustrated in fig. 1, said Y shaft transmission 23 adopts the feed screw nut transmission mechanism.

In embodiment illustrated in fig. 1, said Z shaft transmission 35 is a reductor.

The wire-feed motor 9 that also comprises embodiment illustrated in fig. 1, controller links to each other with wire-feed motor, and wire-feed motor links to each other with welding gun.

The another kind of embodiment of the directed tangent line constant speed of elliptical orbit provided by the invention welding robot device like Fig. 5, Fig. 6, Fig. 7, shown in Figure 8, comprises mechanical arm, Z axle turntable 3, controller 4, the source of welding current 5 and welding gun 6; Said mechanical arm comprises the X axle translation assembly 1 and Y axle translation assembly 2 that is together in series successively; The axis of a weld of workpiece 70 to be welded is an elliptical orbit 71;

Said X axle translation assembly 1 comprises first pedestal 11, X spindle motor 12, X shaft transmission 13 and first slide block 14; The said X spindle motor 12 and first pedestal 11 are affixed, and the output shaft of said X spindle motor 12 links to each other with the input of X shaft transmission 13, and the output of said X shaft transmission 13 links to each other with first slide block 14, and said first slide block 14 slides and is embedded on first pedestal 11;

Said Y axle translation assembly 2 comprises second pedestal 21, second slide block 24 and plane pressing plate 8; Said second pedestal 21 and first slide block 24 are affixed; Said second slide block 24 slides and is embedded on second pedestal 21; The said plane pressing plate 8 and second slide block 24 are affixed; Said plane pressing plate 8 contacts with workpiece 70 tops, and the lower surface of plane pressing plate 8 and elliptical orbit 71 are tangent; The lower surface of said plane pressing plate 8 is a horizontal plane;

Said Z axle turntable 3 comprises the 3rd pedestal 31, Z spindle motor 32, Z shaft transmission 35, joint shaft 33 and workpiece erecting bed 34; Said the 3rd pedestal 31 and first pedestal 11 are affixed; Said Z spindle motor 32 and the 3rd pedestal 31 are affixed; The output shaft of said Z spindle motor 32 links to each other with the input of Z shaft transmission 35; The output of said Z shaft transmission 35 links to each other with joint shaft 33; Said joint shaft 33 is movably set in the 3rd pedestal 31, and said workpiece erecting bed 34 is fixedly sleeved on joint shaft 33;

Said welding gun 6 is fixedly mounted on second slide block 24, and welding gun 6 links to each other with the source of welding current 5; Said X spindle motor 12 links to each other with controller 4 respectively with Z spindle motor 32; Said controller 4 links to each other with the source of welding current 5; Need the workpiece 70 of welding to be fixedly mounted on the workpiece erecting bed 34; The weld seam 71 that has elliptical orbit on the workpiece;

If said first slide block 14 is straight line q with respect to the glide direction of first pedestal 11; If said second slide block 24 is straight line s with respect to the glide direction of second pedestal 21; If the center line of said joint shaft 33 is straight line u; Straight line q, straight line s and straight line u three are vertical in twos; If straight line q and straight line s constitute plane Q ₁, the plane, elliptical orbit 71 place of establishing axis of a weld on the workpiece 70 is plane Q ₂, plane Q ₁With plane Q ₂Overlap;

Controller 4 control X spindle motors 12 rotate with Z spindle motor 32 simultaneously;

As shown in Figure 7, { C}, { initial point of C} is the center O of joint shaft to said world coordinate system to set up world coordinate system _C, world coordinate system { the transverse axis x of C} _CQ is parallel with straight line, x _CThe positive direction of axle is to leave the direction of elliptical orbit 71, also is the positive direction that first slide block 14 slides with respect to first pedestal 11, the world coordinate system { longitudinal axis y of C} _CS is parallel with straight line, y _CThe positive direction of axle is to leave the direction of elliptical orbit 71, also is the positive direction that second slide block 24 slides with respect to second pedestal 21, and { C} and the 3rd pedestal are affixed for this world coordinate system;

{ A}, { initial point of A} is the center O of elliptical orbit to said elliptical coordinate system to set up elliptical coordinate system _A, elliptical coordinate system { the transverse axis x of A} _AOverlap the elliptical coordinate system { longitudinal axis y of A} with transverse _AOverlap with ellipse short shaft, { A} is affixed with the workpiece of band elliptical orbit weld seam for said elliptical coordinate system;

Point O _C{ coordinate figure among the A} is (d in elliptical coordinate system _x, d _y), (d _x, d _y) be known constant; A kind of special case is: the said elliptical coordinate system { longitudinal axis y of A} _ACenter O through said joint shaft _C, then put O _CElliptical coordinate system the coordinate figure among the A} be (0, d _y); Shown in Figure 10 for working as a some O _CAt the elliptical coordinate system { longitudinal axis y among the A} _APositive axis on situation;

If speed of welding is preset value v _w, establishing workpiece 70, to rotate counterclockwise angular speed around joint shaft 33 be ω; If a is major axis half the of said elliptical orbit 71, b is minor axis half the of said elliptical orbit 71, and d is the center O of said elliptical orbit 71 _AWith the joint shaft center O _CDistance; If the major axis of said elliptical orbit 71 and x _CThe angle of axle is θ, 0≤θ≤90 °; The center line of said welding gun 6 and y _CAxle is parallel, and the intersection point of the center line of welding gun 6 and elliptical orbit 71 is solder joint P; { coordinate among the C} is (X to said solder joint P at world coordinate system _C, Y _C); { coordinate among the C} is (X if the distal point T of welding gun 6 is at world coordinate system _TC, Y _TC); The distal point T of said welding gun 6 and the distance of solder joint P are preset value L _aThe distal point T of welding gun 6 and solder joint P are along x _CThe speed of axle equates, is v ₁, relative world coordinate system { C}; The distal point T of welding gun 6 and solder joint P are along y _CThe speed of axle equates, is v ₂, relative world coordinate system { C};

Controller 4 control workpiece 70 satisfy following relationship with welding gun 6:

$X_C=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

$Y_C=\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;},$

X _TC=X _C,

Y _TC=Y _C+L _a,

$\mathrm{\&beta;}=\arctan \left(\frac{Y_C}{X_C}\right),$

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;})}^2}},$

v ₁=Mω，

v ₂=Nω，

Wherein,

$M=\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;},$

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

The directed tangent line constant speed of elliptical orbit of the present invention welding robot device is characterized in that: said X shaft transmission 13 adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

Among second kind of embodiment shown in Figure 5, said X shaft transmission 13 adopts the feed screw nut transmission mechanism.

Among second kind of embodiment shown in Figure 5, said Z shaft transmission 35 is a reductor.

Second kind of embodiment shown in Figure 5 also comprises wire-feed motor 9, and controller links to each other with wire-feed motor, and wire-feed motor links to each other with welding gun.

Second kind of embodiment shown in Figure 5 also comprises spring spare 81, and the two ends of said spring spare connect second slide block and second pedestal respectively; Said spring spare can adopt extension spring, stage clip, torsion spring or sheet spring.Adopt stage clip in the present embodiment.The plane pressing plate that this spring spare makes and second slide block is affixed is near the upper surface elliptical orbit of workpiece.

In conjunction with first kind of embodiment shown in Figure 1 its operation principle is described:

At first, the major axis of the elliptical orbit of workpiece 70 overlaps with horizontal direction.During work, X spindle motor 12, y-axis motor 22 and Z spindle motor 32 rotate simultaneously: X spindle motor 12 rotates, and drives the translation in the horizontal direction of first slide block through X shaft transmission 13; Y-axis motor 22 rotates, and drives second slide block in the vertical direction translation through Y shaft transmission 23; Z spindle motor 32 rotates, and drives joint shaft 33 through Z shaft transmission 35 and rotates, and drives workpiece erecting bed 34 and rotates, and workpiece 70 rotates around the center line of joint shaft 33, and elliptical orbit weld seam 71 rotates around the center line of joint shaft 33.Because each parameter satisfies certain functional relation, therefore can guarantee that the position of solder joint remains at the peak of elliptical orbit, in addition, welding gun is positioned at the downhand position all the time, and promptly the center line of welding gun is always the normal direction of elliptical orbit at this point.Thereby obtain good welding quality.

Second kind of embodiment in conjunction with shown in Figure 5 explains its operation principle:

At first, the major axis of the elliptical orbit of workpiece 70 overlaps with horizontal direction.During work, X spindle motor 12 rotates with Z spindle motor 32 simultaneously: X spindle motor 12 rotates, and drives the translation in the horizontal direction of first slide block through X shaft transmission 13; Z spindle motor 32 rotates, and drives joint shaft 33 through Z shaft transmission 35 and rotates, and drives workpiece erecting bed 34 and rotates, and workpiece 70 rotates around the center line of joint shaft 33, and elliptical orbit weld seam 71 rotates around the center line of joint shaft 33.Because the plane pressing plate is pressed in the elliptical orbit top of workpiece all the time and the lower surface of plane pressing plate is a horizontal plane, therefore no matter how ellipse rotates, and the plane pressing plate is tangential on peak with elliptical orbit all the time; Therefore elliptical orbit is in rotating counterclockwise process; Workpiece can lift the plane pressing plate, thereby lifts second slide block that on second pedestal, is free to slide, and welding gun is lifted; Simultaneously because each parameter satisfies certain functional relation; Welding gun can be moved horizontally to the horizontal level of peak, so the arc length of the distal point of welding gun and solder joint is able to guarantee, and current solder joint is exactly the peak of elliptical orbit.Therefore can guarantee that the position of solder joint remains at the peak of elliptical orbit, in addition, welding gun is positioned at the downhand position all the time, and promptly the center line of welding gun is always the normal direction of elliptical orbit at this point.Thereby obtain good welding quality.

Derivation of equation process combines Fig. 7 to introduce as follows.

(1) target call:

Elliptical orbit on the workpiece

Segmental arc is the welding segmental arc, and current solder joint is P, and P is positioned at

On, included angle=∠ PO _AG ∈ [0 °, 90 °].Require current solder joint P all the time at the peak horizontal tangent place of ellipse, speed of welding is constant to be preset value v _w, the speed of welding direction is oval horizontal tangent direction at this point.

(2) find the solution (X _A, Y _A):

When the workpiece of elliptical orbit weld seam rotated to some angle θ with joint shaft, { coordinate among the A} was (X to solder joint P in elliptical coordinate system _A, Y _A).Elliptic equation is in the A} coordinate system:

$\frac{{X_A}^2}{a^2}+\frac{{Y_A}^2}{b^2}=1.---\left(1\right)$

By elliptical coordinate system A} and world coordinate system translation and the rotation relationship of C} obtain:

$\left\{\begin{array}{c}{X}_A=X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x,\\ Y_A=-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y.\end{array}\right.---\left(2\right)$

(2) formula substitution (1) formula is got:

$\frac{{(X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x)}^2}{a^2}+\frac{{(-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y)}^2}{b^2}=1.---\left(3\right)$

To (3) formula both sides to X _C(this moment, θ was a constant to differential, X _CAnd Y _CBe variable):

$\frac{2}{a^2}(X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x)(\cos \mathrm{\&theta;}+\frac{{\mathrm{dY}}_C}{{\mathrm{dX}}_C}\sin \mathrm{\&theta;})+$

（4）

$\frac{2}{b^2}(-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y)(-\sin \mathrm{\&theta;}+\frac{{\mathrm{dY}}_C}{{\mathrm{dX}}_C}\cos \mathrm{\&theta;})=0.$

Arrangement (4) formula gets

$\frac{{\mathrm{dY}}_C}{{\mathrm{dX}}_C}=\frac{-b^2(X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x)\cos \mathrm{\&theta;}+a^2(-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y)\sin \mathrm{\&theta;}}{b^2(X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x)\sin \mathrm{\&theta;}+a^2(-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y)\cos \mathrm{\&theta;}}.---\left(5\right)$

Because pad and oval tangent peak (assurance downhand position) at ellipse, so:

$\frac{{\mathrm{dY}}_C}{{\mathrm{dX}}_C}=0.---\left(6\right)$

With (6) formula substitution (5) formula,

$\frac{-b^2(X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x)\cos \mathrm{\&theta;}+a^2(-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y)\sin \mathrm{\&theta;}}{b^2(X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x)\sin \mathrm{\&theta;}+a^2(-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y)\cos \mathrm{\&theta;}}=0.---\left(7\right)$

Know that by (7) formula the branch subitem of equal sign left-hand component is zero in (7) formula, that is:

-b ²(X _Ccosθ+Y _Csinθ+d _x)cosθ+a ²(-X _Csinθ+Y _Ccosθ+d _y)sinθ=0. （8）

(2) formula substitution (8) formula is got:

-b ²X _Acosθ+a ²Y _Asinθ=0. （9）

Simultaneous (1) formula must be about X with (9) formula _A, Y _AThe equation with two unknowns group of two unknown numbers:

$\left\{\begin{array}{c}\frac{{X_A}^2}{a^2}+\frac{{Y_A}^2}{b^2}=1,---\left(10a\right)\\ {-b}^2{X}_A\cos \mathrm{\&theta;}+a^2{Y}_A\sin \mathrm{\&theta;}=0.---\left(10b\right)\end{array}\right.$

Get by (10b) formula

$X_A=\frac{a^2\sin \mathrm{\&theta;}}{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2\cos \mathrm{\&theta;}}{Y}_A.---\left(11\right)$

(11) formula substitution (10a) formula is got

$\frac{{\left(\frac{a^2\sin \mathrm{\&theta;}}{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2\cos \mathrm{\&theta;}}{Y}_A\right)}^2}{a^2}+\frac{{Y_A}^2}{b^2}=1.---\left(12\right)$

Because Y _A>=0, get by (12) formula

$Y_A=\frac{b^2}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}.---\left(13\right)$

(13) formula substitution (11) formula is got

$X_A=\frac{a^2\tan \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}.---\left(14\right)$

(13) formula and (14) formula write together be:

$\left\{\begin{array}{c}{X}_A=\frac{a^2\tan \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}},\\ Y_A=\frac{b^2}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}.\end{array}\right.---\left(15\right)$

(3) find the solution (X _C, Y _C) and (X _TC, Y _TC):

When rotating to some angle θ with the workpiece of oval weld seam with joint shaft, { coordinate among the C} is (X to horizontal point of contact (current solder joint) P at world coordinate system _C, Y _C).Have by (formula 2):

$\left\{\begin{array}{c}{X}_A=X_C\cos \mathrm{\&theta;}+Y_C\sin \mathrm{\&theta;}+d_x,---\left(16a\right)\\ Y_A=-X_C\sin \mathrm{\&theta;}+Y_C\cos \mathrm{\&theta;}+d_y.---\left(16b\right)\end{array}\right.$

With the formula * cos θ of (16a) formula * sin θ+(16b),

Y _C=X _Asinθ+Y _Acosθ-d _xsinθ-d _ycosθ. （17）

(17) formula substitution (16a) formula is got

X _A=X _Ccosθ+(X _Asinθ+Y _Acosθ-d _xsinθ-d _ycosθ)sinθ+d _x

Consider sin ²θ+cos ²θ=1, the arrangement following formula gets

X _C=X _Acosθ-Y _Asinθ-d _xcosθ+d _ysinθ （18）

(17) formula and (18) formula are write together, for:

$\left\{\begin{array}{c}{X}_C=X_A\cos \mathrm{\&theta;}-Y_A\sin \mathrm{\&theta;}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},\\ Y_C=X_A\sin \mathrm{\&theta;}+Y_A\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;}.\end{array}\right.---\left(19\right)$

(15) formula substitution (19) formula is got

$\left\{\begin{array}{c}{X}_C=\left(\frac{a^2\tan \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}\right)\cos \mathrm{\&theta;}-\left(\frac{b^2}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}\right)\sin \mathrm{\&theta;}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},\\ Y_C=\left(\frac{a^2\tan \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}\right)\sin \mathrm{\&theta;}+\left(\frac{b^2}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}\right)\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;}.\end{array}\right.$

Promptly

$\left\{\begin{array}{c}{X}_C=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},\\ Y_C=\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;}.\end{array}\right.---\left(20\right)$

Relation by welding gun and solder joint can get

$\left\{\begin{array}{c}{X}_{\mathrm{TC}}=X_C,\\ Y_{\mathrm{TC}}=Y_C+L_a.\end{array}\right.---\left(21\right)$

(4) find the solution β:

Can know by figure:

$\mathrm{\&beta;}=\arctan \left(\frac{Y_C}{X_C}\right).---\left(22\right)$

(5) find the solution speed v ₁, v ₂, ω:

Speed of welding is the relative velocity of welding gun with respect to the elliptical orbit weld seam, under world coordinate system, can be decomposed into two component velocities along transverse axis and y direction.The speed of horizontal point of contact under world coordinate system be exactly need find the solution do

$v_w=\sqrt{{(v_1-v_x)}^2+{(v_2-v_y)}^2}.$

Or be written as:

${\mathrm{<figure-callout\; id="2"\; label="v\; w"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_w^{}={(v_1-v_x)}^2+{(v_2-v_y)}^2.---\left(23\right)$

Wherein, speed of welding v _wBeing preset value, is known constant.

Attention: the speed in (23) formula is algebraic quantity, promptly as velocity attitude and world coordinate system { x among the C} _CAxle or y _CAxle is a positive number when identical, is negative when opposite.

(5.1) about speed v ₁

Because no matter where workpiece turn to, require that current solder joint constantly to overlap with the point of contact all the time, the center line that promptly requires welding gun is the current solder joint (being the point of contact) through carving at that time all the time, thus acquisition high quality welding effect, so the x of the distal point T of welding gun _CAxial velocity v ₁Must equal the x of point of contact P _CAxial velocity promptly has:

${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00001919831000021.png,HDA00001919831000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=\frac{{\mathrm{dX}}_C}{\mathrm{dt}},---\left(24\right)$

In (20) formula substitution (24) formula,

${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00001919831000021.png,HDA00001919831000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=\frac{d[\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;}]}{\mathrm{dt}},$

${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00001919831000021.png,HDA00001919831000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=[(a^2-b^2)\frac{a^2{\tan }^2\mathrm{\&theta;}(\cos \mathrm{\&theta;}-\sec \mathrm{\&theta;})+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;}]\frac{\mathrm{d\&theta;}}{\mathrm{dt}},$

Or be written as:

${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00001919831000021.png,HDA00001919831000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=[\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;}]=\frac{\mathrm{d\&theta;}}{\mathrm{dt}},---\left(25\right)$

For easy, order

$M=\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;}.---\left(26\right)$

Again because,

$\mathrm{\&omega;}=\frac{\mathrm{d\&theta;}}{\mathrm{dt}},---\left(27\right)$

With (26) formula and (27) formula substitution (25) formula,

v ₁=Mω. （28）

(5.2) about speed v ₂

In addition, no matter, require the distal point of welding gun and the distance at point of contact will keep constant all the time because where workpiece turns to, can be constant with the arc length of guaranteeing to weld, thus obtain the high quality welding effect.So y of the distal point T of welding gun _CAxial velocity v ₂Must equal the y of point of contact P _CAxial velocity promptly has:

${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=\frac{{\mathrm{dY}}_C}{\mathrm{dt}},---\left(29\right)$

In (20) formula substitution (29) formula,

${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=\frac{d[\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;}]}{\mathrm{dt}},$

${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=[-\sqrt{a^2{\tan }^2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\sin \mathrm{\&theta;}+\frac{a^2\tan \mathrm{\&theta;}\sec \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;}]\frac{\mathrm{d\&theta;}}{\mathrm{dt}}\text{.}$

Abbreviation gets

${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=[\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;}]\frac{\mathrm{d\&theta;}}{\mathrm{dt}}.---\left(30\right)$

For easy, order

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;}.---\left(31\right)$

With (27) formula and (31) formula substitution (30) formula,

v ₂=Nω. （32）

(5.3) about the speed v of workpiece at the solder joint place _xAnd v _y:

Because workpiece provides in the rotation by joint shaft of the speed at current solder joint place, so have:

$v_x={\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_3\sin \mathrm{\&beta;}=-\mathrm{\&omega;}\left|{\mathrm{PO}}_C\right|\sin \mathrm{\&beta;}=-\mathrm{\&omega;}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;}.---\left(33\right)$

$v_y={\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_3\cos \mathrm{\&beta;}=\mathrm{\&omega;}\left|{\mathrm{PO}}_C\right|\cos \mathrm{\&beta;}=\mathrm{\&omega;}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;}.---\left(34\right)$

(5.4) about the angular velocity omega of joint shaft:

In (28) formula, (32) formula, (33) formula and (34) formula substitution (23) formula,

${\mathrm{<figure-callout\; id="2"\; label="v\; w"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_w^{}={(\mathrm{M\&omega;}+\mathrm{\&omega;}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;})}^2+{(\mathrm{N\&omega;}-\mathrm{\&omega;}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;})}^2.$

Put in order

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{{\mathrm{<figure-callout\; id="2"\; label="X\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_C^{}+{\mathrm{<figure-callout\; id="2"\; label="Y\; C"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_C^{}}\cos \mathrm{\&beta;})}^2}}.---\left(35\right)$

Or be written as:

$\mathrm{\&omega;}=\frac{{\mathrm{<figure-callout\; id="2"\; label="v\; w\; M"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_w}{\sqrt{M^{}}}---\left(36\right)$

After solving ω, be updated to (28), speed v can be obtained in (32) ₁, v ₂

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

(6), utilize the pointwise computational methods to calculate different each value of consult volume constantly based on above-mentioned formula:

Be defined as follows vector:

N is a positive integer, and what representative was controlled counts; Δ t is a time step, i.e. the time interval between two consecutive points;

N-dimensional vector

is the different moment; And t (1)=0, t (i)=(i-1) Δ t, wherein; I=1; 2 ..., n;

N-dimensional vector Major axis and x for elliptical orbit _CThe acute angle, theta sequence that axle is folded, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

Major axis and x for elliptical orbit _CThe acute angle difference Δ θ sequence that axle is folded, and Δ θ (1)=0, Δ θ (j+1)=θ (j+1)-θ (j), wherein, and j=1,2 ..., n-1;

N-dimensional vector

For solder joint P at the world coordinate system { x among the C} _CThe axial coordinate value sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector For solder joint P at the world coordinate system { y among the C} _CThe axial coordinate value sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

For the distal point T of welding gun at the world coordinate system { x among the C} _CThe axial coordinate value sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

For the distal point T of welding gun at the world coordinate system { y among the C} _CThe axial coordinate value sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

Be solder joint P and joint shaft center O _CLine and x _CThe acute angle sequence that axle is folded, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

is an intermediate variable M sequence; Corresponding respectively different t (1) constantly; T (2); ..., t (n);

N-dimensional vector

is an intermediate variable N sequence; Corresponding respectively different t (1) constantly; T (2); ..., t (n);

N-dimensional vector

For the elliptical orbit weld seam around the joint shaft center O _CThe angular velocity omega sequence that rotates counterclockwise, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

Be the linear velocity v of workpiece at solder joint P place ₃At world coordinate system { among the C} along x _CAxle positive direction decomposition rate v _xThe coordinate figure sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

Be the linear velocity v of workpiece at solder joint P place ₃At world coordinate system { among the C} along y _CAxle positive direction decomposition rate v _yThe coordinate figure sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector

For welding gun and solder joint at world coordinate system { among the C} along x _CAxle positive direction linear velocity v ₁The coordinate figure sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n);

N-dimensional vector For welding gun and solder joint at world coordinate system { among the C} along y _CAxle positive direction linear velocity v ₂The coordinate figure sequence, corresponding respectively different t (1) constantly, t (2) ..., t (n).

Adopt following steps to calculate:

(a) given a, b, d, v _w, L _aGiven initial angle θ _Min∈ [0,90 °), given termination point θ _Max∈ (0,90 °], and θ _Max>θ _MinPreset time step delta t; Continue to carry out next step;

(b) i=1; T (1)=0; θ (1)=θ _MinΔ θ (1)=0; Continue to carry out next step;

(c) if i >=2, t (i)=t (i-1)+Δ t, θ (i)=θ (i-1)+Δ θ (i) continue to carry out next step; If i 2, directly carry out next step;

(d) give each vectorial element by following formula each parameter of calculating and assignment successively:

$X_C\left(i\right)=\frac{(a^2-b^2)\sin \mathrm{\&theta;}\left(i\right)}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}\left(i\right)+b^2}}-d_x\cos \mathrm{\&theta;}\left(i\right)+d_y\sin \mathrm{\&theta;}\left(i\right),$

$Y_C\left(i\right)=\sqrt{a^2{\tan }^2\mathrm{\&theta;}\left(i\right)+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\cos \mathrm{\&theta;}\left(i\right)-d_x\sin \mathrm{\&theta;}\left(i\right)-d_y\cos \mathrm{\&theta;}\left(i\right),$

X _TC(i)=X _C(i),

Y _TC(i)=Y _C(i)+L _a,

$\mathrm{\&beta;}\left(i\right)=\arctan \left(\frac{Y_C\left(i\right)}{X_C\left(i\right)}\right),$

$M\left(i\right)=\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;}\left(i\right))\cos \mathrm{\&theta;}\left(i\right)}{(a^2{\tan }^2\mathrm{\&theta;}\left(i\right)+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}\left(i\right)+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}}+d_x\sin \mathrm{\&theta;}\left(i\right)+d_y\cos \mathrm{\&theta;}\left(i\right),$

$N\left(i\right)=\frac{(a^2-b^2)\sin \mathrm{\&theta;}\left(i\right)}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}\left(i\right)+b^2}}-d_x\cos \mathrm{\&theta;}\left(i\right)+d_y\sin \mathrm{\&theta;}\left(i\right)$

$\mathrm{\&omega;}\left(i\right)=\frac{v_w}{\sqrt{{[M\left(i\right)+\sqrt{{\left[X_C\left(i\right)\right]}^2+{\left[Y_C\left(i\right)\right]}^2}\sin \mathrm{\&beta;}\left(i\right)]}^2+{[N\left(i\right)-\sqrt{{\left[X_C\left(i\right)\right]}^2+{\left[Y_C\left(i\right)\right]}^2}\cos \mathrm{\&beta;}\left(i\right)]}^2}},$

v ₁(i)=M(i)·ω(i),

v ₂(i)=N(i)·ω(i),

N=i continues to carry out next step;

(e) if θ (i)+ω (i) Δ t>θ _Max, EP (end of program); If θ (i)+ω (i) Δ t≤θ _Max, continue to carry out next step;

(f) Δ θ (i+1)=ω (i) Δ t continues to carry out next step;

(g) i=i+1 continues execution in step (c).

The aforementioned calculation method has obtained corresponding to difference following each vector constantly:

$\stackrel{\&RightArrow;}{t}=[t\left(1\right),t\left(2\right),...,t\left(n\right)],$ $\stackrel{\&RightArrow;}{\mathrm{\&theta;}}=[\mathrm{\&theta;}\left(1\right),\mathrm{\&theta;}\left(2\right),...,\mathrm{\&theta;}\left(n\right)],$ $\stackrel{\&RightArrow;}{\mathrm{\&Delta;\&theta;}}=[\mathrm{\&Delta;\&theta;}\left(2\right),\mathrm{\&Delta;\&theta;}\left(3\right),...,\mathrm{\&Delta;\&theta;}\left(n\right)],$

$\stackrel{\&RightArrow;}{X_C}=[X_C\left(1\right),X_C\left(2\right),...,X_C\left(n\right)],$ $\stackrel{\&RightArrow;}{Y_C}=[Y_C\left(1\right),Y_C\left(2\right),...,Y_C\left(n\right)],$

$\stackrel{\&RightArrow;}{X_{\mathrm{TC}}}=[X_{\mathrm{TC}}\left(1\right),X_{\mathrm{TC}}\left(2\right),...,X_{\mathrm{TC}}\left(n\right)],$ $\stackrel{\&RightArrow;}{Y_{\mathrm{TC}}}=[Y_{\mathrm{TC}}\left(1\right),Y_{\mathrm{TC}}\left(2\right),...,Y_{\mathrm{TC}}\left(n\right)],$

$\stackrel{\&RightArrow;}{\mathrm{\&beta;}}=[\mathrm{\&beta;}\left(1\right),\mathrm{\&beta;}\left(2\right),...,\mathrm{\&beta;}(n)],$ $\stackrel{\&RightArrow;}{\mathrm{\&omega;}}=[\mathrm{\&omega;}\left(1\right),\mathrm{\&omega;}\left(2\right),...,\mathrm{\&omega;}\left(n\right)],$

$\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA00001919831000021.png,HDA00001919831000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1}=[v_1\left(1\right),v_1\left(2\right),...,v_1\left(n\right)],$ $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00001919831000011.png,HDA00001919831000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2}=[v_2\left(1\right),v_2\left(2\right),...,v_2\left(n\right)].$

Providing one group of real data below specifies.

Suppose given a=600mm, b=300mm, d _x=0mm, d _y=50mm, v _w=6mm/s, L _a=8mm; Given initial angle θ _Min=10 °, given termination point θ _Max=80 °, preset time step delta t=1s.

Then can calculate the result, each variable θ, ω, X through above-mentioned pointwise computational methods _C, Y _C, v ₁, v ₂With time relation curve such as Figure 12, Figure 13, Figure 14, shown in Figure 15.The partial data value is as shown in table 1.

Each variable θ of table 1, ω, X _C, Y _C, v ₁, v ₂Calculated value (selected parts)

This device adopts the Three Degree Of Freedom mechanism of self-movement to realize workpiece elliptical orbit weld seam high-quality welding function, and when adopting this device to weld, welding gun is on the elliptical orbit weld seam normal at the pad place all the time; Welding direction is the tangential direction of elliptical orbit; And towards preestablishing on certain fixed-direction, it is constant that speed of welding keeps all the time for this tangent line, and welding quality is high; Efficient is high, and the manufacturing of device, maintenance and use cost are low; Because the every bit in welding, the weld seam solder joint on welding gun and the workpiece all remains a kind of relative position and attitude, therefore can reach the high-quality welding effect of optimization; The direction that sets can be an any direction, for example: when elliptical orbit is on the vertical facade, welding gun is kept in the vertical direction, and welding direction remains and go up in the horizontal direction, thereby obtain the high-quality welding effect of downhand position; For example: when elliptical orbit is on the horizontal plane, welding gun and welding direction is all remained simultaneously go up in the horizontal direction, thereby obtain the high-quality welding effect of horizontal position.

Claims (10)

1. the directed tangent line constant speed of an elliptical orbit welding robot device is characterized in that: comprise mechanical arm, Z axle turntable (3), controller (4), the source of welding current (5) and welding gun (6); Said mechanical arm comprises X axle translation assembly (1) and the Y axle translation assembly (2) that is together in series successively; The axis of a weld of workpiece to be welded is an elliptical orbit;

Said X axle translation assembly comprises first pedestal (11), X spindle motor (12), X shaft transmission (13) and first slide block (14); The said X spindle motor and first pedestal are affixed, and the output shaft of said X spindle motor links to each other with the input of X shaft transmission, and the output of said X shaft transmission links to each other with first slide block, and said first slide block slides and is embedded on first pedestal;

Said Y axle translation assembly comprises second pedestal (21), y-axis motor (22), Y shaft transmission (23) and second slide block (24); Said second pedestal and first slide block are affixed; The said y-axis motor and second pedestal are affixed, and the output shaft of said y-axis motor links to each other with the input of Y shaft transmission, and the output of said Y shaft transmission links to each other with second slide block, and said second slide block slides and is embedded on second pedestal;

Said Z axle turntable comprises the 3rd pedestal (31), Z spindle motor (32), Z shaft transmission (35), joint shaft (33) and workpiece erecting bed (34); Said the 3rd pedestal and first pedestal are affixed; Said Z spindle motor and the 3rd pedestal are affixed; The output shaft of said Z spindle motor links to each other with the input of Z shaft transmission; The output of said Z shaft transmission links to each other with joint shaft, and said joint shaft is movably set in the 3rd pedestal, and said workpiece erecting bed is fixedly sleeved on joint shaft;

Said welding gun is fixedly mounted on second slide block, and welding gun links to each other with the source of welding current; Said X spindle motor, y-axis motor and Z spindle motor link to each other with controller respectively; Controller control X spindle motor, y-axis motor and Z spindle motor rotate simultaneously; Said controller links to each other with the source of welding current; Need the workpiece of welding to be fixedly mounted on the workpiece erecting bed; The weld seam that has elliptical orbit on the workpiece; If said first slide block is straight line q with respect to the glide direction of first pedestal; If said second slide block is straight line s with respect to the glide direction of second pedestal; If the center line of said joint shaft is straight line u; Straight line q, straight line s and straight line u three are vertical in twos; If straight line q and straight line s constitute plane Q ₁, the plane, elliptical orbit place of establishing axis of a weld on the workpiece is plane Q ₂, plane Q ₁With plane Q ₂Overlap;

{ C}, { initial point of C} is the center O of joint shaft to said world coordinate system to set up world coordinate system _C, world coordinate system { the transverse axis x of C} _CQ is parallel with straight line, x _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that first slide block slides with respect to first pedestal, the world coordinate system { longitudinal axis y of C} _CS is parallel with straight line, y _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that second slide block slides with respect to second pedestal, and { C} and the 3rd pedestal are affixed for this world coordinate system; { A}, { initial point of A} is the center O of elliptical orbit to said elliptical coordinate system to set up elliptical coordinate system _A, elliptical coordinate system { the transverse axis x of A} _AOverlap the elliptical coordinate system { longitudinal axis y of A} with transverse _AOverlap with ellipse short shaft, { A} is affixed with the workpiece of band elliptical orbit weld seam for said elliptical coordinate system; Point O _C{ coordinate figure among the A} is (d in elliptical coordinate system _x, d _y), (d _x, d _y) be known constant;

If speed of welding is preset value v _w, establishing workpiece, to rotate counterclockwise angular speed around joint shaft be ω; If a is major axis half the of said elliptical orbit, b is minor axis half the of said elliptical orbit; If the major axis of said elliptical orbit and x _CThe angle of axle is θ, 0≤θ≤90 °; The center line of said welding gun and y _CAxle is parallel, and the center line of welding gun and the intersection point of elliptical orbit are solder joint P; { coordinate among the C} is (X to said solder joint P at world coordinate system _C, Y _C); { coordinate among the C} is (X if the distal point T of welding gun is at world coordinate system _TC, Y _TC); The distal point T of said welding gun and the distance of solder joint P are preset value L _aThe distal point T of welding gun and solder joint P are along x _CThe speed of axle equates, is v ₁, relative world coordinate system { C}; The distal point T of welding gun and solder joint P are along y _CThe speed of axle equates, is v ₂, relative world coordinate system { C};

Controller satisfies following relationship through control control workpiece and welding gun:

$X_C=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

$Y_C=\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;},$

X _TC=X _C,

Y _TC=Y _C+L _a,

$\mathrm{\&beta;}=\arctan \left(\frac{Y_C}{X_C}\right),$

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{X_C^2+Y_C^2}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{X_C^2+Y_C^2}\cos \mathrm{\&beta;})}^2}},$

v ₁=Mω，

v ₂=Nω，

Wherein,

$M=\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;},$

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

2. the directed tangent line constant speed of elliptical orbit as claimed in claim 1 welding robot device, it is characterized in that: said X shaft transmission adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

3. the directed tangent line constant speed of elliptical orbit as claimed in claim 1 welding robot device, it is characterized in that: said Y shaft transmission adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

4. the directed tangent line constant speed of elliptical orbit as claimed in claim 1 welding robot device, it is characterized in that: said Z shaft transmission (35) is a reductor.

5. the directed tangent line constant speed of elliptical orbit as claimed in claim 1 welding robot device, it is characterized in that: also comprise wire-feed motor (9), controller links to each other with wire-feed motor, and wire-feed motor links to each other with welding gun.

6. the directed tangent line constant speed of an elliptical orbit welding robot device is characterized in that: comprise mechanical arm, Z axle turntable (3), controller (4), the source of welding current (5) and welding gun (6); Said mechanical arm comprises X axle translation assembly (1) and the Y axle translation assembly (2) that is together in series successively; The axis of a weld of workpiece to be welded is an elliptical orbit;

Said X axle translation assembly comprises first pedestal (11), X spindle motor (12), X shaft transmission (13) and first slide block (14); The said X spindle motor and first pedestal are affixed, and the output shaft of said X spindle motor links to each other with the input of X shaft transmission, and the output of said X shaft transmission links to each other with first slide block, and said first slide block slides and is embedded on first pedestal;

Said Y axle translation assembly comprises second pedestal (21), second slide block (24) and plane pressing plate (8); Said second pedestal and first slide block are affixed; Said second slide block slides and is embedded on second pedestal; The said plane pressing plate and second slide block are affixed; Said plane pressing plate contacts with workpiece, and the lower surface and the elliptical orbit of plane pressing plate are tangent; The lower surface of said plane pressing plate is a horizontal plane;

Said Z axle turntable comprises the 3rd pedestal (31), Z spindle motor (32), Z shaft transmission (35), joint shaft (33) and workpiece erecting bed (34); Said the 3rd pedestal and first pedestal are affixed; Said Z spindle motor and the 3rd pedestal are affixed; The output shaft of said Z spindle motor links to each other with the input of Z shaft transmission; The output of said Z shaft transmission links to each other with joint shaft, and said joint shaft is movably set in the 3rd pedestal, and said workpiece erecting bed is fixedly sleeved on joint shaft;

Said welding gun is fixedly mounted on second slide block, and welding gun links to each other with the source of welding current; Said X spindle motor links to each other with controller respectively with the Z spindle motor; Controller control X spindle motor and Z spindle motor rotate simultaneously; Said controller links to each other with the source of welding current; Need the workpiece of welding to be fixedly mounted on the workpiece erecting bed; The weld seam that has elliptical orbit on the workpiece; If said first slide block is straight line q with respect to the glide direction of first pedestal; If said second slide block is straight line s with respect to the glide direction of second pedestal; If the center line of said joint shaft is straight line u; Straight line q, straight line s and straight line u three are vertical in twos; If straight line q and straight line s constitute plane Q ₁, the plane, elliptical orbit place of establishing axis of a weld on the workpiece is plane Q ₂, plane Q ₁With plane Q ₂Overlap;

{ C}, { initial point of C} is the center O of joint shaft to said world coordinate system to set up world coordinate system _C, world coordinate system { the transverse axis x of C} _CQ is parallel with straight line, x _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that first slide block slides with respect to first pedestal, the world coordinate system { longitudinal axis y of C} _CS is parallel with straight line, y _CThe positive direction of axle is to leave the direction of elliptical orbit, also is the positive direction that second slide block slides with respect to second pedestal, and { C} and the 3rd pedestal are affixed for this world coordinate system; { A}, { initial point of A} is the center O of elliptical orbit to said elliptical coordinate system to set up elliptical coordinate system _A, elliptical coordinate system { the transverse axis x of A} _AOverlap the elliptical coordinate system { longitudinal axis y of A} with transverse _AOverlap with ellipse short shaft, { A} is affixed with the workpiece of band elliptical orbit weld seam for said elliptical coordinate system; Point O _C{ coordinate figure among the A} is (d in elliptical coordinate system _x, d _y), (d _x, d _y) be known constant;

If speed of welding is preset value v _w, establishing workpiece, to rotate counterclockwise angular speed around joint shaft be ω; If a is major axis half the of said elliptical orbit, b is minor axis half the of said elliptical orbit; If the major axis of said elliptical orbit and x _CThe angle of axle is θ, 0≤θ≤90 °; The center line of said welding gun and y _CAxle is parallel, and the center line of welding gun and the intersection point of elliptical orbit are solder joint P; { coordinate among the C} is (X to said solder joint P at world coordinate system _C, Y _C); { coordinate among the C} is (X if the distal point T of welding gun is at world coordinate system _TC, Y _TC); The distal point T of said welding gun and the distance of solder joint P are preset value L _aThe distal point T of welding gun and solder joint P are along x _CThe speed of axle equates, is v ₁, relative world coordinate system { C}; The distal point T of welding gun and solder joint P are along y _CThe speed of axle equates, is v ₂, relative world coordinate system { C};

Controller control workpiece and welding gun satisfy following relationship:

$X_C=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

$Y_C=\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}\cos \mathrm{\&theta;}-d_x\sin \mathrm{\&theta;}-d_y\cos \mathrm{\&theta;},$

X _TC=X _C,

Y _TC=Y _C+L _a,

$\mathrm{\&beta;}=\arctan \left(\frac{Y_C}{X_C}\right),$

$\mathrm{\&omega;}=\frac{v_w}{\sqrt{{(M+\sqrt{X_C^2+Y_C^2}\sin \mathrm{\&beta;})}^2+{(N-\sqrt{X_C^2+Y_C^2}\cos \mathrm{\&beta;})}^2}},$

v ₁=Mω，

v ₂=Nω，

Wherein,

$M=\frac{(a^2-b^2)(b^2-a^2{\tan }^4\mathrm{\&theta;})\cos \mathrm{\&theta;}}{(a^2{\tan }^2\mathrm{\&theta;}+b^2)\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}+d_x\sin \mathrm{\&theta;}+d_y\cos \mathrm{\&theta;},$

$N=\frac{(a^2-b^2)\sin \mathrm{\&theta;}}{\sqrt{a^2{\tan }^2\mathrm{\&theta;}+b^2}}-d_x\cos \mathrm{\&theta;}+d_y\sin \mathrm{\&theta;},$

The relation of said θ and time t is the integration of ω; Behind the initial angle of having preset initial time, can calculate the relation of θ and time t through the pointwise computational methods based on above-mentioned formula.

7. the directed tangent line constant speed of elliptical orbit as claimed in claim 6 welding robot device, it is characterized in that: said X shaft transmission adopts feed screw nut transmission mechanism, rack and pinion drive mechanism, tape handler, chain drive or rope transmission mechanism.

8. the directed tangent line constant speed of elliptical orbit as claimed in claim 6 welding robot device, it is characterized in that: said Z shaft transmission (35) is a reductor.

9. the directed tangent line constant speed of elliptical orbit as claimed in claim 6 welding robot device, it is characterized in that: also comprise wire-feed motor (9), controller links to each other with wire-feed motor, and wire-feed motor links to each other with welding gun.

10. the directed tangent line constant speed of elliptical orbit as claimed in claim 6 welding robot device; It is characterized in that: also comprise spring spare (81); The two ends of said spring spare connect second slide block and second pedestal respectively, and said spring spare adopts extension spring, stage clip, torsion spring or sheet spring.

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